The present invention relates to an X-ray imaging method and device for observing or testing an object having a plurality of layers, more particularly, a package structure of an electronic device having a plurality of soldering layers by detecting an X-ray transmission image thereof.
A transmission image of an object can be commonly obtained by irradiating the object with an electromagnetic wave such as an X-ray or a particle beam such as an .alpha.-ray and .beta.-ray and detecting the transmission intensity thereof. The X-ray image is a typical example of such a transmission image.
Such a transmission image had a disadvantage that when a plurality of objects are superposed, it is frequently difficult to decide the front-rear relation thereof by the human eye. In order to obviate this disadvantage, a technique of separately detecting the respective objects with respect to differences among their depths by applying the depth information extraction technique by binocular vision to the X-ray transmission image has been proposed in the Proceedings of the 24th Annual Conference of the Society of Instrument and Control Engineers (1985) pp. 845-846.
The above binocular vision is a technique in which an object image is detected from two points apart from each other by a certain distance and the distance to the object is detected from the parallaxes of the image from the two directions.
In the prior art, as shown in FIG. 1, first, a group of objects are rotated by a minute angle .DELTA..theta. around the axis. The rotation axis perpendicular to the transmission direction and two transmission images before the rotation and after the rotation are detected. This corresponds the objects that are binocularly visioned as shown in FIG. 2. It is understood from the comparison of two transmission images that the respective objects are shifted by minute amounts corresponding to their depths in the transmission angle. Therefore, the depth information of the respective objects can be obtained from the differences in the shift amounts.
More specifically, the depth amount h(x) in the above prior art is calculated as follows.
Both transmission images f.sub.1 (x) and f.sub.2 (x) can be approximated as ##EQU1## where D=H sin.DELTA..theta.
H: distance between the said axis and the
position of the detecting device
Taking a difference between f.sub.1 (x) and f.sub.2 (x), ##EQU2##
Assuming that the spacial change in h(x) is smooth and the size of the object is negligibly smaller than the distance H, the differentiation in the x-direction is ##EQU3##
Thus, h(x) is obtained and so the depth information is obtained from the the transmission images.
In this way, the prior ar extracts the depth information from two detected transmission images of objects rotated by a minute angle .DELTA..theta. and separately judges the objects by the differences in depth. In this method, in the approximation of equations (1) and (2), it is assumed that ##EQU4##
Therefore, as the size of an object is smaller with respect to the depth amount h(x), the rotation angle .DELTA..theta. must be as so sufficiently reduced. However, as .DELTA..theta. becomes small, the difference between f.sub.1 (x) and f.sub.2 (x), i.e. the value of equation (3) becomes also small. This means that the accuracy in the depth amount h(x) obtained by equation (3) is reduced. Accordingly, the above prior art has an advantage that the method thereof is not applicable unless the size of an object is sufficiently larger than the depth amount to be detected.
Another prior art will be explained below. An X-ray transmission image is obtained by irradiating an object with X-rays and two-dimensionally detecting the intensity of tee detected X-rays. Commonly, the detection is carried out by directly taking the X-ray image on a film or indirectly taking the fluorescence emitted when the X-rays fall onto a fluorescent plate. The detection is also performed by converting the X-ray image into an optical image using an image intensifier and taking the optical image by e.g. a television camera to be detected as electrical signals.
The X-ray transmission image permits the part directly invisible from the outside to be detected. However, if substances are three-dimensionally superposed, all the substances are superposedly detected on the same image, so that it was frequently difficult to discrimintte the superposed portions from only the transmission image. There has been proposed in JP-A-57-61937 a method of detecting X-ray images using plural X-rays with different photon energies and processing these images to extract an image of a particular portion, thereby making it easy to observe the superposed substances. This method will be explained briefly.
Now, the model as shown in FIG. 3 is taken for X-ray transmission. It is assumed that an object consisting of a substance X 59 having a thickness of X and a substance Y 60 having a thickness of y which are superposed is irradiated with an X-ray e having an intensity I.sub.e and an X-ray f having an intensity of I.sub.f and the transmission X-ray intensities I.sub.e and I.sub.f are obtained. The X-ray e and the X-ray f are two X-rays with different photon energies. Further, it is assumed that the X-rays having a single wavelength are irradiated, and the X-ray absorption coefficients of substance X 59 and substance Y 60 for the X-ray e are .mu..sub.Xe and .mu..sub.Ye, and likewise the X-ray absorption coefficients of substance X 59 and substance Y 60 for the x-ray f are .mu..sub.Xf and .mu..sub.Yf. FIG. 4 is a graph showing the relation between the X-ray absorption coefficient and Y-ray photon energy for lead (Pb) and tungsten (W). If the substance X 59 is lead and the substance Y 60 is tungsten while the X-ray e and the X-ray f are shown as FIG. 4, .mu..sub.Xe, .mu..sub.Xf, .mu..sub.Ye and .mu..sub.Yf are different constants as shown in FIG. 4.
Then, the following equations hold. EQU I.sub.e =I.sub.o exp(-.mu..sub.Xe x-.mu..sub.Ye y) (6) EQU I.sub.f =I.sub.o exp(-.mu..sub.Xf x-.mu..sub.Yf y) (7)
Solving these equations with respect to x, ##EQU5## This value indicates the thickness of the substance X. Therefore, if two X-ray transmission mmages are detected by using the X-ray e and the X-ray f and the above computations are carried out for all the corresponding points, an image indicative of the thickness of only the substance X 59 can be detected.
Now it should be noted in the above prior art that the irradiation of the X-ray with a single wavelength (monochromatic X-ray) is assumed, and so the change of the quality of the X-ray which will occur when the X-ray is transmitted through a substance has been neglected. However, it is difficult to use the monochromatic X-ray in actually detecting X-ray transmission images, and the irradiated X-ray has a photon energy spectrum which is continuous in a certain range. Then, the X-ray changes in its quality when it is transmitted through the substance so that equations (6) and (7) in which the X-ray absorption coefficients are assumed to be constant do not hold. Even if the thickness is obtained from equation (8), it will contain an error.
Further, a method for describing X in equation (8) using higher degree polynominals with respect to the terms of I.sub.n (I.sub.e /I.sub.o) and I.sub.n (I.sub.f /I.sub.o) but not by linea expressions has been proposed in IEEE Trans. Nucl. Sci. NS-27, No. 2 (1980) pp 961-968. However, this method, which performs an approximation by secondary or third order polynominals, does not also provide the result with high accuracy if non-linearity of X concerning each of I.sub.n (I.sub.e /I.sub.o) and I.sub.n (I.sub.f /I.sub.o) is too great.